Related papers: Automatic Unbounded Verification of Alloy Specific…
We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…
Large language models (LLMs) often generate reasoning traces that appear coherent but rest on unsupported assumptions, leading to hallucinated conclusions. Prior work mainly addresses factual hallucinations or relies on post-hoc…
Recent work on activation and latent steering has demonstrated that modifying internal representations can effectively guide large language models (LLMs) toward improved reasoning and efficiency without additional training. However, most…
The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem…
We present an approach to automatically synthesize synchronized models from lightweight formal specifications. Our approach takes as input a specification of a distributed system along with a global linear time constraint, which must be…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Logical specifications are widely used to represent software systems and their desired properties. Under system degradation or environmental changes, commonly seen in complex real-world robotic systems, these properties may no longer hold…
We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning. While simple and effective, adding theory axioms can also pollute the search space with many irrelevant…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
Incorrectness Separation Logic (ISL) is a proof system designed to automate verification and detect bugs in programs manipulating heap memories. In this study, we extend ISL to support variable-length array predicates and pointer…
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The key difficulty is verification: suggested proofs may look…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…